Rank-Restricted Hierarchical Alternating Least Squares Algorithm for Matrix Completion with Applications

The matrix completion problem aims to recover missing entries in a partially observed matrix by approximating it with a low-rank structure. The two common approaches—the singular value thresholding and matrix factorization with alternating least squares—often become prohibitively expensive for large...

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Vydané v:Applied sciences Ročník 15; číslo 16; s. 8876
Hlavný autor: Lee, Geunseop
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 01.08.2025
Predmet:
Algorithms
Approximation
Deep learning
Efficiency
hierarchical alternating least squares
image completion
Lagrange multiplier
Liu, Timothy
Machine learning
matrix completion
Optimization
recommender system
Recommender systems
singular value thresholding
Sparsity
ISSN:2076-3417, 2076-3417
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Popis
Shrnutí:The matrix completion problem aims to recover missing entries in a partially observed matrix by approximating it with a low-rank structure. The two common approaches—the singular value thresholding and matrix factorization with alternating least squares—often become prohibitively expensive for large matrices or when rigorous accuracy is demanded. To address these issues, we propose a rank-restricted hierarchical alternating least squares with orthogonality and sparsity constraints, which includes a novel shrinkage function. Specifically, for faster execution speed, truncated factor matrices are updated to restrict the costly shrinkage step as well as boundary-condition heuristics. Experiments on image completion and recommender systems show that the proposed method converges with extremely fast execution speed while achieving comparable or superior reconstruction accuracy relative to state-of-the-art matrix completion methods. For example, in the image completion problem, the proposed algorithm produced outputs approximately 15 times faster on average than the most accurate reference algorithm, while achieving 98% of its accuracy.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2076-3417
2076-3417
DOI:10.3390/app15168876